Higher June 2022 Paper 3 Q20
20 £2448 is invested in an account at a rate of compound interest.
One year after the investment there is £2496.96 in the account.
How much is in the account four years after the investment? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(2496.96 \div 2448\) or 1.02 | M1 | implied by correct value for 2, 3 or 4 years |
| \(2496.96 \times (\text{their } 1.02)^3\) or \(2448 \times (\text{their } 1.02)^4\) or 2649.79… | M1dep | oe eg full year by year method shown |
| 2649.77 or 2649.78 or 2649.79 or 2649.8(0) | A1 | accept 2650(.00) with M2 awarded SC2 2702.78 or 2702.79 or 2702.8(0) |
| Alternative method 2 | ||
| \((2496.96 - 2448) \div 2448\) or \(48.96 \div 2448\) or 0.02 or 2% | M1 | |
| \(2496.96 \times \left(1 + \dfrac{\text{their } 2}{100}\right)^3\) or \(2448 \times \left(1 + \dfrac{\text{their } 2}{100}\right)^4\) or 2649.79… | M1dep | oe eg full year by year method shown |
| 2649.77 or 2649.78 or 2649.79 or 2649.8(0) | A1 | accept 2650(.00) with M2 awarded SC2 2702.78 or 2702.79 or 2702.8(0) |
Additional guidance
| Calculated by year, the amounts would be: 2 years 2546.89 or 2546.90 3 years 2597.82 or 2597.83 or 2597.84 | |
| Condone 2650.0 | M1M1A1 |
| 2546.89, 2597.83, 2649.78, 2702.77 do not award A mark if further work seen after correct answer | M1M1A0 |
| \(\dfrac{48.96}{2496.96} \times 100 = 2\%\) is incorrect working | M0M0A0 |